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Reaction–Diffusion Modeling of E. coli Colony Growth Based on Nutrient Distribution and Agar Dehydration

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Abstract

The bacterial colony is a powerful experimental platform for broad biological research, and reaction–diffusion models are widely used to study the mechanisms of its formation process. However, there are still some crucial factors that drastically affect the colony growth but are not considered in the current models, such as the non-homogeneously distributed nutrient within the colony and the substantially decreasing expansion rate caused by agar dehydration. In our study, we propose two plausible reaction–diffusion models (the VN and MVN models) based on the above two factors and validate them against experimental data. Both models provide a plausible description of the non-homogeneously distributed nutrient within the colony and outperform the classical Fisher–Kolmogorov equation and its variation in better describing experimental data. Moreover, by accounting for agar dehydration, the MVN model captures how a colony’s expansion slows down and the change of a colony’s height profile over time. Furthermore, we demonstrate the existence of a traveling wave solution for the VN model.

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Acknowledgements

This work was supported by the National Institutes of Health (NIH) under Grant 5R01GM131405 and the US National Science Foundation (NSF) Rules of Life program DEB-1930728.

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Author notes

  1. Changhan He and Lifeng Han have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, Irvine, CA, USA

    Changhan He

  2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA

    Lifeng Han, Duane C. Harris & Yang Kuang

  3. School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, USA

    Samat Bayakhmetov & Xiao Wang

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  1. Changhan He
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  2. Lifeng Han
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  3. Duane C. Harris
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  5. Xiao Wang
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  6. Yang Kuang
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Correspondence to Changhan He.

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He, C., Han, L., Harris, D.C. et al. Reaction–Diffusion Modeling of E. coli Colony Growth Based on Nutrient Distribution and Agar Dehydration. Bull Math Biol 85, 61 (2023). https://doi.org/10.1007/s11538-023-01163-2

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